Robust State Feedback Control Through Actuators With Generalized Sector Nonlinearities And Saturation

In control systems, actuators often have nonlinear characteristics that can not be neglected. For linear systems driven by actuators satisfying the generalized sector condition, a robust state feedback controller synthesis method is proposed to achieve the ultimate boundedness control. The method is based on the linear matrix inequality approach and is easy to apply. As an important special case of the generalized sector condition, the saturation characteristic of actuators is discussed separately, and non‐conservative results are obtained.     

PI control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. In this paper, we exploit their unique physical structure to show how two term, i.e. proportional plus integral (or PI) action, can be used to control these processes to produce desired behavior (as opposed to just stability).     

Stability analysis and antiwindup design of uncertain discrete-time switched linear systems subject to actuator saturation

This paper investigates the stability analysis and antiwindup design problem for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the switched Lyapunov function approach.Supposing that a set of linear dynamic output controllers have been designed to stabilize the switched system without considering its input saturation,we design antiwindup compensation gains in order to enlarge the domain of attraction of the closed-loop system in the presence of saturation.Then,in terms of a sector condition,the antiwindup compensation gains which aim to maximize the estimation of domain of attraction of the closed-loop system are presented by solving a convex optimization problem with linear matrix inequality(LMI)constraints.A numerical example is given to demonstrate the effectiveness of the proposed design method.     

具有时变状态滞后2-D离散系统的稳定与镇定(英文)

针对一类由局部状态空间(LSS)Fornasini-Marchesini(FM)第二模型描述的,具有时变状态滞后的2-D离散系统,其中时变滞后项的上、下界均为正实数,研究了其稳定性和控制综合问题。首先,利用Lyapunov-Krasovski泛函方法,提出了系统的稳定性准则。再根据这一准则,分别设计状态反馈和动态输出反馈控制器保证系统的稳定性。状态反馈控制律和输出反馈矩阵可由线性矩阵不等式(LMI)求得。最后,通过数值算例说明所得结果的有效性。     

Asymptotic and robust stability of T‐S fuzzy genetic regulatory networks with time‐varying delays

In this paper, we propose and investigate a new general model of fuzzy genetic regulatory networks described by the Takagi–Sugeno (T‐S) fuzzy model with time‐varying delays. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the delayed fuzzy genetic regulatory networks are expressed as a set of LMIs, which can be solved numerically by LMI toolbox in Matlab. Two fuzzy genetic network example are given to verify the effectiveness and applicability of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Observer‐based Reliable Control for Discrete Time Systems: An Average Dwell Time Approach

This paper deals with the problem of reliable control for discrete time systems with actuator failures. The actuator is assumed to fail occasionally and can recover over a time interval. During the time of suffering failures, the considered closed‐loop system is assumed unstable. Using an average dwell time method and under the condition that the activation time ratio between the system without actuator failures and the system with actuator failures is not less than a specified constant, an observer‐based feedback controller is developed in terms of linear matrix inequalities such that the resulting closed‐loop system is exponentially stable. An example is included to demonstrate the effectiveness of the proposed approach.     

不确定离散系统的鲁棒Gl2滤波器设计

对于凸多面体不确定离散系统,研究了满足误差估计系统鲁棒稳定且满足一定Gl₂性能指标的线性全阶稳定滤波器设计方法.分别给出了确定性和不确定性离散系统具有Gl₂性能的线性矩阵不等式（linear matrix inequality, LMI)充要条件和充分条件.在此基础上,通过使用滤波器参数化方法,分别推导出了以LMI描述的确定性和不确定性系统的Gl₂滤波器存在的充要条件和充分条件,进而可以使用LMI凸优化程序求解滤波器.通过对算例的计算,结果表明,在噪声信号为独立范数有界情况下,鲁棒Gl₂滤波比H_∞滤波具有更少的保守性.     

A new calculation method of feedback controller gain for bilinear paper-making process with disturbance

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.     

Stability analysis and controller synthesis for discrete uncertain singular fuzzy systems with distinct difference matrices in the rules

This paper mainly studies an extended discrete singular fuzzy model incorporating the multiple difference matrices in the rules and discusses its stability and design issues. By embracing additional algebraic constraint, traditional discrete Takagi-Sugeno (T-S) fuzzy model can be extended to a generalised discrete singular Takagi-Sugeno (GDST-S) model with individual difference matrices E_i in the locally singular models, where it can describe a larger class of physical or non-linear systems. Based on the linear matrix inequality (LMI) approach, we focus on deriving some explicit stability and design criteria expressed by the LMIs for the regarded system. Thus, the stability verification and controller synthesis can be performed by the current LMI tools. Finally, some illustrative examples are given to illustrate the effectiveness and validity of the proposed approach.     

Sliding mode control for Markov jump linear uncertain systems with partly unknown transition rates

In this paper, based on sliding mode control approach, the robust stabilisation problem for a class of continuous-time Markovian jump linear uncertain systems with partly unknown transition rates is investigated. The transition rate matrix under consideration covers completely known, boundary known and completely unknown elements. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. Then a sliding mode control law is designed to drive the state trajectory of the closed-loop system to the specified linear switching surface in finite time in spite of the existing uncertainties and unknown transition rates. Finally, an example is given to verify the validity of the theoretical results.